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source: branches/f4grobner/monomial.lisp@ 764

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1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22;;----------------------------------------------------------------
23;; This package implements BASIC OPERATIONS ON MONOMIALS
24;;----------------------------------------------------------------
25;; DATA STRUCTURES: Conceptually, monomials can be represented as lists:
26;;
27;; monom: (n1 n2 ... nk) where ni are non-negative integers
28;;
29;; However, lists may be implemented as other sequence types,
30;; so the flexibility to change the representation should be
31;; maintained in the code to use general operations on sequences
32;; whenever possible. The optimization for the actual representation
33;; should be left to declarations and the compiler.
34;;----------------------------------------------------------------
35;; EXAMPLES: Suppose that variables are x and y. Then
36;;
37;; Monom x*y^2 ---> (1 2)
38;;
39;;----------------------------------------------------------------
40
41(defpackage "MONOMIAL"
42 (:use :cl)
43 (:export "MONOM"
44 "EXPONENT"
45 "MAKE-MONOM"
46 "MONOM-ELT"
47 "MONOM-DIMENSION"
48 "MONOM-TOTAL-DEGREE"
49 "MONOM-SUGAR"
50 "MONOM-DIV"
51 "MONOM-MUL"
52 "MONOM-DIVIDES-P"
53 "MONOM-DIVIDES-MONOM-LCM-P"
54 "MONOM-LCM-DIVIDES-MONOM-LCM-P"
55 "MONOM-LCM-EQUAL-MONOM-LCM-P"
56 "MONOM-DIVISIBLE-BY-P"
57 "MONOM-REL-PRIME-P"
58 "MONOM-EQUAL-P"
59 "MONOM-LCM"
60 "MONOM-GCD"
61 "MONOM-DEPENDS-P"
62 "MONOM-MAP"
63 "MONOM-APPEND"
64 "MONOM-CONTRACT"
65 "MONOM-EXPONENTS"))
66
67(in-package :monomial)
68
69(deftype exponent ()
70 "Type of exponent in a monomial."
71 'fixnum)
72
73(defstruct (monom
74 ;; BOA constructor
75 (:constructor make-monom (dimension
76 &key
77 (initial-exponents #() initial-exponents-supplied-p)
78 (initial-exponent #() initial-exponent-supplied-p)
79 (exponents (cond
80 ;; when exponents are supplied
81 (initial-exponents-supplied-p
82 (make-array (list dimension) :initial-contents initial-exponents
83 :element-type 'exponent))
84 ;; when all exponents are to be identical
85 (initial-exponent-supplied-p
86 (make-array (list dimension) :initial-element initial-exponent
87 :element-type 'exponent))
88 ;; otherwise, all exponents are zero
89 (t (make-array (list dimension) :element-type 'exponent :initial-element 0)))))))
90 (exponents nil :type (vector exponent *)))
91
92;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
93;;
94;; Operations on monomials
95;;
96;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
97
98(defun monom-dimension (m)
99 (declare (type monom m))
100 (length (monom-exponents m)))
101
102(defmacro monom-elt (m index)
103 "Return the power in the monomial M of variable number INDEX."
104 `(elt (monom-exponents ,m) ,index))
105
106(defun monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
107 "Return the todal degree of a monomoal M. Optinally, a range
108of variables may be specified with arguments START and END."
109 (declare (type monom m) (fixnum start end))
110 (reduce #'+ (monom-exponents m) :start start :end end))
111
112(defun monom-sugar (m &aux (start 0) (end (monom-dimension m)))
113 "Return the sugar of a monomial M. Optinally, a range
114of variables may be specified with arguments START and END."
115 (declare (type monom m) (fixnum start end))
116 (monom-total-degree m start end))
117
118(defun monom-div (m1 m2 &aux (result (copy-structure m1)))
119 "Divide monomial M1 by monomial M2."
120 (declare (type monom m1 m2))
121 (map-into (monom-exponents result) #'- (monom-exponents m1) (monom-exponents m2))
122 result)
123
124(defun monom-mul (m1 m2 &aux (result (copy-structure m1)))
125 "Multiply monomial M1 by monomial M2."
126 (declare (type monom m1 m2 result))
127 (map-into (monom-exponents result) #'+ (monom-exponents m1) (monom-exponents m2))
128 result)
129
130(defun monom-divides-p (m1 m2)
131 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
132 (declare (type monom m1 m2))
133 (every #'<= (monom-exponents m1) (monom-exponents m2)))
134
135(defun monom-divides-monom-lcm-p (m1 m2 m3)
136 "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
137 (declare (type monom m1 m2 m3))
138 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z)))
139 (monom-exponents m1)
140 (monom-exponents m2)
141 (monom-exponents m3)))
142
143(defun monom-lcm-divides-monom-lcm-p (m1 m2 m3 m4)
144 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
145 (declare (type monom m1 m2 m3 m4))
146 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (<= (max x y) (max z w)))
147 (monom-exponents m1)
148 (monom-exponents m2)
149 (monom-exponents m3)
150 (monom-exponents m4)))
151
152(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
153 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
154 (declare (type monom m1 m2 m3 m4))
155 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (= (max x y) (max z w)))
156 (monom-exponents m1)
157 (monom-exponents m2)
158 (monom-exponents m3)
159 (monom-exponents m4)))
160
161(defun monom-divisible-by-p (m1 m2)
162 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
163 (declare (type monom m1 m2))
164 (every #'>= (monom-exponents m1) (monom-exponents m2)))
165
166(defun monom-rel-prime-p (m1 m2)
167 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
168 (declare (type monom m1 m2))
169 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y)))
170 (monom-exponents m1)
171 (monom-exponents m2)))
172
173(defun monom-equal-p (m1 m2)
174 "Returns T if two monomials M1 and M2 are equal."
175 (declare (type monom m1 m2))
176 (every #'= (monom-exponents m1) (monom-exponents m2)))
177
178(defun monom-lcm (m1 m2 &aux (result (copy-structure m1)))
179 "Returns least common multiple of monomials M1 and M2."
180 (declare (type monom m1 m2))
181 (map-into (monom-exponents result) #'max
182 (monom-exponents m1)
183 (monom-exponents m2))
184 result)
185
186(defun monom-gcd (m1 m2 &aux (result (copy-structure m1)))
187 "Returns greatest common divisor of monomials M1 and M2."
188 (declare (type monom m1 m2))
189 (map-into (monom-exponents result) #'min (monom-exponents m1) (monom-exponents m2))
190 result)
191
192(defun monom-depends-p (m k)
193 "Return T if the monomial M depends on variable number K."
194 (declare (type monom m) (fixnum k))
195 (plusp (monom-elt m k)))
196
197(defmacro monom-map (fun m &rest ml &aux (result `(copy-structure ,m)))
198 `(map-into (monom-exponents ,result) ,fun ,m ,@ml))
199
200(defmacro monom-append (m1 m2)
201 `(make-monom (+ (monom-dimension ,m1) (monom-dimension ,m2))
202 :initial-exponents (concatenate 'list (monom-exponents ,m1) (monom-exponents ,m2))))
203
204(defmacro monom-contract (k m)
205 `(setf (monom-exponents ,m) (subseq (monom-exponents ,m) ,k)))
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